Q 11-07-014JEE MainAIEEE 2011Medium
Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is
Answer: (A) $-\dfrac{9Gm}{r}$
Null point at distance $x$ from $m$: $\dfrac{Gm}{x^2} = \dfrac{G(4m)}{(r - x)^2} \Rightarrow r - x = 2x \Rightarrow x = \dfrac{r}{3}$.
$$V = -\frac{Gm}{r/3} - \frac{G(4m)}{2r/3} = -\frac{3Gm}{r} - \frac{6Gm}{r} = -\frac{9Gm}{r}$$
Solution by Sreeraj P, M.Sc Physics